{"as_of":"2026-08-10T20:19:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5176d61a9374b42a9a49eb92323652d09dd3fa05ed12248162e54ae80efed851","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T22:44:06.804417Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2508.06740/citation-record","integrity":"/paper/2508.06740/integrity","json":"/paper/2508.06740/citation-record.json","paper":"/paper/2508.06740"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.385313Z","title":"Hyperplane arrangement face algebras and their associated Markov chains","venue":null,"work_id":"a7945320-c018-4a6d-bb8d-8434d9a99e18","year":1997},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.685155Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:beeafcb5e013c9488ccd1fa6163e3441ce38eb5d9cea9ea9e0782a306c309a9b","observation_id":"b5ce8f96-0903-48b5-999b-0692e0d606ab","resolution":{"observed_at":"2026-08-05T22:44:07.389839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.370005Z","title":"Noncommutative character theory of the symmetric group","venue":null,"work_id":"499b8cb4-61ec-4f49-91de-b9eca7118232","year":2005},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.691379Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:d666f7597305ce0ff1bc4a82fa1303ddefba8a48ac78f2400b5c5d05964e6069","observation_id":"770497d3-b2b3-4c26-b9ed-3d30c279f52b","resolution":{"observed_at":"2026-08-05T22:44:07.375378Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.356019Z","title":"Semigroup and ring theoretical methods in probability","venue":null,"work_id":"dadd6d6a-baac-42f4-976e-d00e684b37eb","year":2002},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.695863Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:56001d49f0f95c3656a54e1937f355c03ff5add89ceecb78f49260ad9ffd2f34","observation_id":"309e1879-5952-43db-a949-9da276c3deb9","resolution":{"observed_at":"2026-08-05T22:44:07.360524Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1023/a:1007822931408","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Semigroups, rings, and Markov chains","venue":"Journal of Theoretical Probability","work_id":"fe9598cd-f45c-4b09-b408-f7ee0af9760e","year":2000},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.700387Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:f681147226988e373332a43c8ab4ba5b7e72402eee41f4b06ca05dbfceb0a50d","observation_id":"9a40378e-204b-46ac-9601-d07b69628999","resolution":{"observed_at":"2026-08-05T22:44:06.900410Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.341488Z","title":"Mathematical developments from the analysis of riffle shuffling","venue":null,"work_id":"72feab0d-57e7-4b7d-b6c4-17ae44ec89a0","year":2001},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.705322Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:a4bd368a17496dc3db74f5097e73eb44713dc9c5893512a1991fff34bf77df88","observation_id":"91c79929-5d58-4ffe-a80c-d6620605c1ac","resolution":{"observed_at":"2026-08-05T22:44:07.346236Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/mbk/146","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"The mathematics of shuffling cards","venue":"American Mathematical Society eBooks","work_id":"13fbf489-d641-4f62-9ac7-8f0413cf3723","year":2023},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.710037Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:da2af520d1b35d5ce2c59da0a74f29948379204dec52a6ba0d46fe093eb891e5","observation_id":"a59ad7a6-a38c-498b-9baa-e370dae6883e","resolution":{"observed_at":"2026-08-05T22:44:06.884920Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.326146Z","title":"Generating a random permutation with random transpositions","venue":null,"work_id":"7fe64b9d-412e-4616-819b-762398da1fb0","year":1981},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.716450Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:7d5d1fd6bb42fcba350210877c52aaa16e431ac14b88183a62bf72976970ffa0","observation_id":"4b962bb5-823f-4de2-892e-0828c99eb901","resolution":{"observed_at":"2026-08-05T22:44:07.331082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.312092Z","title":"Spectral analysis of random-to-random Markov chains","venue":null,"work_id":"2ec6f2cd-5009-434d-8933-fecaf45f22f4","year":2018},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.721621Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:57ee041883af8cfa252449c43b29bb9a406f47442b7e6654bef0d80f91dd6c5e","observation_id":"9e63d914-27a0-430e-8b0e-818b3fd54f3c","resolution":{"observed_at":"2026-08-05T22:44:07.316497Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.00738","last_updated":"2025-05-31T22:58:31Z","snapshot_observed_at":"2026-08-10T04:30:05.938298Z","submitted_at":"2025-05-31T22:58:31Z","title":"An Introduction to Algebraic Combinatorics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.00738","snapshot_observed_at":"2026-08-05T22:44:06.725858Z","title":"An Introduction to Algebraic Combinatorics","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.725858Z"},"links":{"cited_paper":"/paper/2506.00738","citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:79fc71a1e30f6d91ee572fe41085cc26692bd542abafc29983dea998a35da89c","observation_id":"eefd3faf-1750-4736-9ee8-b63160e3da65","resolution":{"observed_at":"2026-08-05T22:44:06.725858Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.297389Z","title":"Is this sum of cycles invertible in QSn? MathOverflow","venue":null,"work_id":"27ee73ea-c577-4c5e-bd8b-59f5b6571ff4","year":2025},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.730535Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:acf0de7c789f52309d1e38a3965b1712da9246a4184884576a94b817d8eb66d7","observation_id":"16c021ad-0efd-49c8-a947-f65dd9578b5d","resolution":{"observed_at":"2026-08-05T22:44:07.302478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.282764Z","title":"The one-sided cycle shuffles, and other mysteries and wonders of the symmetric group algebra [talk slides]","venue":null,"work_id":"cf0da7cd-9b51-4eb4-88ec-c277d0526795","year":2025},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.734700Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:7eaa83c74da764a34f872823484190f0b87b62f08a9d366fc3b9a279374b0e7d","observation_id":"243089ac-e2a2-4d32-a5bd-8ad74c7206f7","resolution":{"observed_at":"2026-08-05T22:44:07.287473Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2212.06274","last_updated":"2024-03-10T22:35:24Z","snapshot_observed_at":"2026-08-10T04:30:56.794315Z","submitted_at":"2022-12-12T22:50:40Z","title":"The one-sided cycle shuffles in the symmetric group algebra","version":4},"cited_work":{"arxiv_id":"2212.06274","doi":null,"metadata_source":"pith","pith_arxiv_id":"2212.06274","snapshot_observed_at":"2026-08-05T22:44:07.101801Z","title":"The one-sided cycle shuffles in the symmetric group algebra","venue":"math.CO","work_id":"fbebfc09-7c04-406b-8c89-baf0d90ce75f","year":2022},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.739128Z"},"links":{"cited_paper":"/paper/2212.06274","citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:d27e03ee12e2c49efd3a7287b1dda8a023ed5c404153c0e5e11c641a426fa1cc","observation_id":"664581da-1d5a-4f83-9208-61a410a6fbb0","resolution":{"observed_at":"2026-08-05T22:44:07.106369Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.01118","last_updated":"2026-06-05T20:11:33Z","snapshot_observed_at":"2026-07-06T16:13:42.284158Z","submitted_at":"2023-09-03T08:35:21Z","title":"The enriched $q$-monomial basis of the quasisymmetric functions","version":4},"cited_work":{"arxiv_id":"2309.01118","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.01118","snapshot_observed_at":"2026-08-05T22:44:07.082216Z","title":"The enriched $q$-monomial basis of the quasisymmetric functions","venue":"math.CO","work_id":"14c4232e-9ea2-4579-b014-451123e3edc8","year":2023},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.743724Z"},"links":{"cited_paper":"/paper/2309.01118","citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:490dab8625f0f2e87a253922a89f3c2e70878da2ad7c9d1a21f4996810d64b75","observation_id":"980d8127-b1ce-4b70-bf57-ff0f2825f7a7","resolution":{"observed_at":"2026-08-05T22:44:07.086656Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.268422Z","title":"A semigroup approach to wreath-product extensions of Solomon’s descent algebras","venue":null,"work_id":"298da662-b44b-4d6a-98df-f643adee43df","year":2009},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.748320Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:98a7c723d3301da2d2dbb739bf72d5738940cf3d4f0c448525363f013e174376","observation_id":"084c02f2-55cc-45d6-ae10-7762b7238daa","resolution":{"observed_at":"2026-08-05T22:44:07.272998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1134/s0016266324020072","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"The miracle of integer eigenvalues","venue":"Functional Analysis and Its Applications","work_id":"827895dc-d1d7-453d-ba65-4f5d7322f66a","year":2024},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.757645Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:c2b3d170968765bafb42bb9de2b4f2600af8ba1203e1e450cf79260c87c422e0","observation_id":"818afdb2-47b7-43d6-ace3-95fa30c2215c","resolution":{"observed_at":"2026-08-05T22:44:06.868348Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/s0218196797000113","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Noncommutative symmetric functions. II: Transformations of alphabets","venue":"International Journal of Algebra and Computation","work_id":"b43cad85-1ced-43a8-9742-a7aa404464e7","year":1997},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.761980Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:6ca0e7869f1a8c95ee12f5ca0e1dd23485a60719cedc0740f0032d91bf742403","observation_id":"50cf9419-e284-4fb7-a23f-8f86f45eee94","resolution":{"observed_at":"2026-08-05T22:44:06.853829Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:06.766274Z","title":"A tour of representation theory","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.766274Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:5096253a455090ed3d65f82264993be2d32d8447872b4ee802ba823ce6324ff0","observation_id":"884cb1e6-4748-427c-8727-df8d180a3e5c","resolution":{"observed_at":"2026-08-05T22:44:06.766274Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.238910Z","title":"On the matrix occurring in a linear search problem","venue":null,"work_id":"8e1d1290-ee72-4445-98cd-e6a01c8f4947","year":1991},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.770772Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:2f86a631d7dab1c255e7a316090262634ee5e015b51c9ff2a9877711df3ae7b2","observation_id":"c239de5c-9e17-456a-a68a-1a99c7dba688","resolution":{"observed_at":"2026-08-05T22:44:07.243855Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1102.2460","last_updated":"2011-04-21T14:49:12Z","snapshot_observed_at":"2026-07-06T02:23:24.557986Z","submitted_at":"2011-02-11T23:31:37Z","title":"Spectra of Symmetrized Shuffling Operators","version":2},"cited_work":{"arxiv_id":"1102.2460","doi":null,"metadata_source":"pith","pith_arxiv_id":"1102.2460","snapshot_observed_at":"2026-08-05T22:44:07.060114Z","title":"Spectra of Symmetrized Shuffling Operators","venue":"math.CO","work_id":"056be192-a3df-4c76-a105-fb177c4b1b1e","year":2011},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.775125Z"},"links":{"cited_paper":"/paper/1102.2460","citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:9c094171b19d55c04565d35bed57b8778012b8f59d650d6c95205ceda12e5a80","observation_id":"035e3f1c-039e-49f5-b468-3bdd6e704ab0","resolution":{"observed_at":"2026-08-05T22:44:07.065490Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.223442Z","title":"Iterated-Integral Signatures in Machine Learning","venue":null,"work_id":"669df294-ae80-4b92-93ba-bec07855078e","year":2019},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.779624Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:1d67468abd2edbf6f4b94044c0d4a8f69a0f59df12dc94d23518308e8a55a1fe","observation_id":"62898a4c-2d53-44bc-a94a-d01ef7aa3c5d","resolution":{"observed_at":"2026-08-05T22:44:07.228231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.207649Z","title":null,"venue":null,"work_id":"6daa6992-1463-42f6-91a7-203097898252","year":2020},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.783706Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:ebe15f649c536ee607f962d80906ad28097d324a35a01f13bb53a47cfdf9be66","observation_id":"29a7a82b-f794-4471-bb1b-9a2c5a89a5cc","resolution":{"observed_at":"2026-08-05T22:44:07.211921Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.192957Z","title":"Hyperplane arrangements and descent algebras","venue":null,"work_id":"dc56c649-6fcd-485d-be34-501e9eca495b","year":null},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.787986Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:14af7e25076e8b114248752f840c79c46871c9b85448b575a1bd8d323aa78f32","observation_id":"036dfe36-05e2-47c0-9a4d-f9bcd0b9e58e","resolution":{"observed_at":"2026-08-05T22:44:07.197526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.162565Z","title":"The descent algebra of the symmetric group","venue":null,"work_id":"e6bd42ae-422b-4cb7-95e3-4acd7a8cf9ee","year":2002},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.792381Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:af9d80c5d45f461604671e101f7243a77144d6406ffa39de6a1e9501cd825ba1","observation_id":"3b9505a8-54cb-4a86-ae6a-56552f8da364","resolution":{"observed_at":"2026-08-05T22:44:07.171056Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.146687Z","title":"A Mackey formula in the group ring of a Coxeter group","venue":null,"work_id":"b7977578-2aaf-4425-a4ca-727cbe7e2e7e","year":1976},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.796558Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:4f6b388e802e0bd7681775adb973763f6650cb0e6cee9947ad145776d8c19f6a","observation_id":"9677b20a-6c5d-489e-a462-7e396a302870","resolution":{"observed_at":"2026-08-05T22:44:07.151594Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.132267Z","title":null,"venue":null,"work_id":"a59f8197-567b-45b3-8479-a33c64da2c67","year":2011},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.800527Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:b26ffd16ac110fa33870202ec0a055d160390cc5d3e40ac2047341619b683b7d","observation_id":"f8977393-dfd3-4c82-8da1-20ce037dee13","resolution":{"observed_at":"2026-08-05T22:44:07.136539Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"aspm/0141012","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.037330Z","title":null,"venue":null,"work_id":"b13e7513-a47c-4f5b-a66e-2dac3d841278","year":1986},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.804417Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:683d048ae7b3d228d6c23c7f6efcb76961f0c637b4e8fecc2de1a224bda4d3d0","observation_id":"e72d8857-5620-4de6-b05d-563b4ecc0fe0","resolution":{"observed_at":"2026-08-05T22:44:07.044872Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:44:07.253863Z","title":null,"venue":null,"work_id":"ff4b5945-e11f-43dc-81d9-ca1faf5291ea","year":null},"citing_paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle","version":1},"reference_index":8926,"source":"pdf_text","source_observed_at":"2026-08-05T22:44:06.753142Z"},"links":{"citing_paper":"/paper/2508.06740"},"observation_digest":"sha256:66ed80441fc9f6a6d12b25552ae1bc18aec4e837b0370f5cc3764f8f1108f0ae","observation_id":"83ca855f-4018-4f76-934b-367f867d7abe","resolution":{"observed_at":"2026-08-05T22:44:07.258247Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.06740","last_updated":"2025-08-08T22:36:30Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-10T04:30:24.309236Z","submitted_at":"2025-08-08T22:36:30Z","title":"Top to random and reverse: analysis of a new descent algebra shuffle"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":8,"verified_fuzzy":12},"total_outbound_references":27},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2508.06740."}